Question

A convergent doublet of separated lens, corrected for spherical aberration, are separated by $2 \,cm$ and has an equivalent focal length of $10 \,cm$. The focal length of its component lenses are:

• A. $ f_{1}=18\,cm,\,f_{2}=10\,cm $
• B. $f_{1}=20 \,cm , f_{2}=28\, cm$
• C. $f_{1}=20 \,cm , f_{2}=18 \,cm$
• D. $f_{1}=24 \,cm , f_{2}=18 \,cm$

Answer 1

Answer: (C)

Since, the doublet is corrected for spherical.
aberration, it satisfies the following condition.
$f_{1}-f_{2}=d=2\, cm$
$ \Rightarrow f_{1}=f_{2}+2 \,m$
Let the equivalent focal length $=F: F$
$=\frac{f_{1} f_{2}}{f_{1}+f_{2}=d}=10 \,cm$
Solving it, $f_{1}= 20 \,cm , f_{2}=18\, cm .$